It seems to be rotting, but I doubt that gash is to blame, especially as the bulk of the rot is on the other side, and coming up from the base.
How often do you water it? If it's more than once every two weeks, then it's probably too much. Over-watering may be to blame for it rotting.
Seeing as it seems to be rotting from the base up, it will certainly die.
Just to double check, are the brown bits soft? Also, turn the cactus out of its pot and check the roots. If it is healthy, there should be plenty and they should be plump and white or beige in colour. If they are brown and/or shrivelled, and generally few in number, then they have died.
Assuming the roots and base of the cactus are rotting, the only way to save it is to try and take a cutting from the healthy tissue on top. Remove it from its pot and take a clean, sharp knife. Cut the top off the cactus, taking care only to get healthy tissue (no brown bits). Cut at least 0.5cm above any brown, just to be sure.
Then leave the cut top somewhere dry and airy for three or four days, until the cut edge as dried and callused. Then repot it into moist, very free draining (50% grit, ideally) potting compost. Water a little every time the soil completely dried out (not just dry on the surface). Do not feed. Within a month or so it should hopefully have grown new roots.